Let W denote the words in the English dictionary

• Relations Functions

Let W denote the words in the English dictionary. Define the relation R by:

R = {(x, y) ε W × W | the words x and y have at least one letter in common}. Then R is

1. reflexive, symmetric and not transitive
2. reflexive, symmetric and transitive
3. not reflexive, symmetric and transitive
4. reflexive, not symmetric and transitive

Answer

Given relation R such that

R = {(x, y) ε W × W | the word x and y have at least one letter in common} where W denotes set of words in English dictionary

Clearly (x ,x ) ε R for all x ε W

Therefore, (x, x) has every letter common, therefore R is reflexive

Let (x, y) ε R then (y, x) ε R as x and y have atleast one letter in common, this implies, R is symmetric.

But R is not transitive, Let x = DON, y = NEST, z = SHE

The correct option is A.